an asymmetric (e.g. public-key) cryptosystem, based on modular exponentiation with big exponents and modulus. RSA can be used both for signature and encryption.

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Is there an upper bound to the private exponent in RSA?

In the RSA algorithm, we choose $p$ and $q$ as prime numbers and we select a value $e$ which is coprime to $\varphi(pq)=(p-1)(q-1)$. Then we calculate $d:=e^{-1}\bmod\varphi(pq)$. My question is: ...
1
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1answer
95 views

How is RSA able to prevent brute forcing using the public key?

Bob calculates a private and public key. Bob sends his public key to John. Jeff is a third party unwanted member and manages to snatch the public key mid-transfer. John encrypts his message ...
90
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4answers
58k views

Why is elliptic curve cryptography not widely used, compared to RSA?

I recently ran across elliptic curve crypto-systems: An Introduction to the Theory of Elliptic Curves (Brown University) Elliptic Curve Cryptography (Wikipedia) Performance analysis of identity ...
0
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2answers
188 views

How is message length involved in public/private-key encryption?

I've just read this question regarding why to sign only the hash of a message. I kind of understood the answer, but the question arisen is now: Why can I encrypt any text messages with the same ...
0
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1answer
935 views

generate RSA public key having public modulus and exponent [closed]

i want to generate an RSA public public key file using openssl (or other tools) having public modulus and exponent, so i can use it later to encrypt files i have this: ...
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0answers
36 views

Is it possbile to get same set of public and private keys twice while creating CSR ? If so where does the conflict happens !?

I'm new to cryptography and please clarify if my below assumption is wrong. Lets assume, that two different banks creating CSR and they get identical public and private key pairs of RSA. In such ...
5
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1answer
412 views

Timing Attack on RSA

So far I have researched on timing attack on RSA, We all know the ransomware named Cryptolocker it uses RSA 2048 bit encryption. Now is it possible to break the encryption using timing attack. I have ...
1
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1answer
208 views

Shared modulus attack on RSA

Consider a scenario in which a group of people use a common modulus $n$ in the textbook RSA crypto system, where $n=pq$, $p$ and $q$ are large distinct prime numbers. Is there any chance for an ...
3
votes
1answer
92 views

How to understand RSA Proofs of correctness at Wikipedia

From Wikipedia(https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29#Proofs_of_correctness): $m^{ed}$ ≡ $m$ $\pmod{q}$ $m^{ed}$ ≡ $m$ $\pmod{p}$ then $m^{ed}$ ≡ $m$ $\pmod{pq}$ Question: if $m^{ed}$ ...
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3answers
567 views

Does RSA operate over a Finite Field (Galois Field)?

Is it correct to say that RSA operates over a Finite Field (Galois Field)? In this case GF(p)? I do understant that the modulo in RSA is not itself a prime number, but all the operations ...
4
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1answer
77 views

Adding two RSA private key

We've constructed a new private RSA key from two known private RSA keys $Priv_1$ and $Priv_2$ as follows: $$p = next\underline{}prime\left(\frac{Priv_1(p) + Priv_2(p)}{2}\right)$$ and $$q = ...
2
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0answers
102 views

Limit the number of private key uses for RSASSA-PKCS1-v1_5 with SHA-256 signature?

Assuming all messages and their signatures are available to the attacker, is it secure to use the same RSA private key to sign many messages (roughly $10^{6}$) via PKCS#11 ...
0
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0answers
16 views

In the RSA encryption system, are there not multiple messages m that give the same cipher text c? [duplicate]

For example: p = 5, q = 11, n = 55 $\phi$(55) = 40 e = 3, $\phi$(55) and 3 are relatively prime m = 3, then: $3^3 mod(55) = 27$ m = 113, then: $113^3 mod(55) = 27$ I heard that e and $\phi$(n) ...
1
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1answer
172 views

How to determine the RSA Private key size from the Public.key file?

Question: How to determine the RSA Private key size from the Public.key file? Just roughly, how big it could be? ...
0
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1answer
152 views

1024 RSA Hash Signature attack. Forge a valid signature

I have an RSA signature of 1024 bit where i know the following: Public modulus N Public exponent (0x03) Cypher message Summary: An MD5 hash is calculated from a collection of byte and is used as ...
2
votes
1answer
58 views

Why can we ignore $y$ when using the extended Euclidean algorithm to calculate an RSA decryption exponent?

I have a follow-up question about the extended Euclidean algorithm, as applied to RSA key generation, described in this answer. Let us say we have $p=5$, $q=11$ and $e=17$, so that $N=55$ and ...
0
votes
1answer
47 views

How to deliver an encrypted message to multiple recipients without revealing keys

Let's say I have generated a private and a public key. I create a message and encrypt it with the public key. I deliver this encrypted message and a private key to multiple recipients. Why would I do ...
2
votes
2answers
480 views

Is it safe to reuse a symmetric key when using asymmetric encryption?

I've written a C# Library that I hope will be used for security purposes in a commercial application. The application will communicate through the internet and not on an internal network. I am using ...
2
votes
2answers
375 views

RSA: Is it secure to use the private key to encrypt and the public key to decrypt?

This may sound weird: What if I don't let others know my public key, then use my private key to encrypt, and the public key to decrypt? Is this secure? Let me explain a little bit: Common usuage: ...
3
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0answers
30 views

Authenticate encrypted seed for KEM + AEAD hybrid cryptosystem

Say I want to encrypt something using RSA / KEM and an authenticated cipher. I encrypt using the following scheme: generate random seed z using ...
1
vote
1answer
79 views

If my server utilises an RSA based certificate, why does firefox think I am using Diffie Hellman?

I am not a beginner in crypto, but not that far from it, so please be gentle. I look after a web server app that I generated the SSL certificate for, and I used an RSA public/private keypair. When ...
5
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1answer
273 views

Using same modulus for RSA

I know that there exist some attack when using same modulus. Can two different pairs of RSA key have the same modulus? RSA cracking: The same message is sent to two different people problem But ...
18
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1answer
7k views

Security strength of RSA in relation with the modulus size

NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits: ...
3
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2answers
1k views

Generate RSA-2048 private key for a VERY fast decryption (don't care if it will be unsecure)

Given public standard RSA exponent e = 65537, is there any (d, n) pairs so that RSA decryption becomes a trivial operation? The modulus n must be no less than 2048-bit. The goal is to get a real ...
2
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1answer
87 views

Is there really any way to nullify or avoid MITM attacks?

The question pretty much sums it up. Is there any way to make an attacker who is successfully performing an MITM attack to actually not be able to read or change the messages? Assuming there is no ...
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1answer
44 views

Authenticating with a document

Hope you're having a nice day. I need to implement an authentication system between a "document" (it's not exactly a document, but an object without any computing capacity, only able to store ...
27
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2answers
2k views

What security authorities and standards reject $e=3$ in RSA, when, and with what rationale?

In RSA, some security authorities and/or standards allow the public exponent $e=3$, others require or recommend $e>2^{16}$ (or perhaps some other minimum). I gathered the following: PKCS#1 allows ...
2
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1answer
195 views

RSA - PKCS#1 padding - overall correction of algorithm

From PKCS#1, page 24: After we create the EM byte string and convert it to an integer, we then encrypt that integer with RSAEP (page 10) to get the ciphertext (as an integer). My question arrives ...
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0answers
94 views

CPA-security proof of “l-padded RSA” encryption scheme

The 10.9 exercise from the Katz-Lindell textbook creates a lot of confusion, let me state it here. Consider the following experiment for an algorithm $A$ and a function $l$ with $l(n) \leq 2n-2$ for ...
8
votes
1answer
117 views

Can RSA be securely used for “blind decryption”?

Assume we have the following setup: A client with trusted storage and computing capabilities (e.g. a smartcard) A server with trusted computing and short-term storage capabilities (e.g. RAM + CPU, ...
0
votes
2answers
189 views

Assemble RSA keys from components [closed]

I'm studying openpgp cryptography and struggling to understand some things. I can't use pgp tool for generating keys and ecryption, but have to write a simple app to generate keys, encrypt and decrypt ...
3
votes
4answers
3k views

Why is RSA encryption significantly faster than decryption?

I am designing an implementation of RSA . I recorded computation times in Java by using System.currentTimeMillis(). It returned an encryption time of 0.05 ms and ...
6
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1answer
1k views

CKM_RSA_PKCS vs CKM_RSA_X_509 mechanisms in PKCS#11

What is the exact difference between the CKM_RSA_PKCS and CKM_RSA_X_509 mechanisms in the PKCS#11 v2.20 specification (Please ...
3
votes
1answer
550 views

Recommended password complexity for SSH key encryption using AES-256-CBC

When protecting SSH private keys with password-based encryption, what would be a good minimum password complexity+length standard to make cracking the password too difficult to be worthwhile anytime ...
2
votes
1answer
120 views

Why isn't a table used to solve the large number factoring problem?

Lots of modern encryption (RSA comes to mind) are based on the fact that factoring large numbers is hard. However, multiplying large numbers is much easier, and table lookups are very easy. Since ...
8
votes
4answers
1k views

Is it possible to get an RSA encryption key by comparing the unencrypted and encrypted file?

Exactly what the title says. If I have a RSA encrypted file, and the exact same file but decrypted, can I tell the key that was used from that information?
5
votes
2answers
775 views

How to verify the integrity of RSA encrypted messages?

I need to encrypt messages using PublicKeyCrypto and send it to the server, where the message should be decrypted. I'm aware of the Padding Oracle Attack and want to apply a server side integrity ...
3
votes
1answer
158 views

Is RSA vulnerable to the padding oracle attack?

I know that AES in combination with CBC mode is vulnerable against the Padding Oracle Attack. RSA also uses some kind of padding, hence can this attack be apply to RSA encrypted messages too?
11
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2answers
242 views

Attacking RSA signature verification that ignores padding

I am looking at a RSA signature verification that is quite obviously flawed and am wondering if there's a way to exploit that flaw in practice. Signature is generated using RSA with PKCS 1.5 padding, ...
2
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2answers
72 views

How badly does disclosing an M-bit prefix of an N-bit private key compromise security?

I apologize profusely for knowing nothing about cryptography, please go easy on me! I'm working on a project where I have a 2048-bit RSA private key and a public certificate generated from the ...
6
votes
1answer
393 views

What does “a 15360-bit RSA key is the equivalent to a 256-bit symmetric key” mean?

NIST key management guidelines suggest that 15360-bit RSA keys are equivalent in strength to 256-bit symmetric keys. If a 15360-bit RSA key is the equivalent to a 256-bit symmetric key, does that mean ...
1
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1answer
82 views

Difference between RSA-617 and RSA-2048

according to wikipedia: RSA-617 has 617 decimal digits (2,048 bits). RSA-2048 has 617 decimal digits (2,048 bits). What is the main difference between them?
3
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0answers
48 views

IND-CCA1 RSA padding?

I've found a way to complete a task which I'd solve with passwords or by sending keys over the wire (otherwise) by using RSA's homomorphic property. I'm restricted to RSA (any padding; for hardware ...
2
votes
1answer
128 views

Security impact of signing small data using RSA

I have an application which consists of a client and a server. Both have a pair of public and private key (RSA). For communication, both sign their messages and send them to the other part. So a ...
1
vote
1answer
251 views

Unblind a RSA blinded signature

I have blinded $m = 16$ with $r= 13$, $e = 7$ and $n = 209$. This resulted in $m' = 464$, which led to a $s' = 8$. Now, I want to unblind this $s'$ by using $s = s' \times r^{-1}$ but im stuck at ...
14
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4answers
4k views

Is it possible to validate a Public Key in RSA?

If I have a 1024-bit number, and someone is telling me that it is in fact a valid RSA public key, is there any way I can quickly validate that it is indeed so (without cracking RSA)? (I suppose I am ...
6
votes
1answer
8k views

How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?
0
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1answer
70 views

RSA signature attack check on lowest 16 bytes - Implementation

I am referring to solution given in this question I need help to implement Poncho hint in this comment: As the first question i have an RSA signature of 1024 bit applied on an hash (MD5) of the ...
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1answer
89 views

RSA problem - how to find $d$ [duplicate]

For example, let $p = 3$ and $q= 11$, choose $e = 3$. What computation I have to apply in order to find the corresponding $d$? I know it's 7, but I want to know the exact process to be applied to find ...
21
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2answers
11k views

Definition of Textbook RSA

What is the definition of Textbook RSA? What are some of the properties of textbook RSA? How does it differ from other RSAs?